1. The Role Of Internal Degrees Of Freedom In Reactions With Composite Systems Naureen Ahsan, Alexander Volya Florida State University

2. m2m2 m1m1 x1x1 x2x2 The composite object The External Potential: Intrinsic Potential: Energy levels: Incident wave (Intrinsic energy ħω/2, total energy E) Transmission Reflection CM Momentum: Description of the System

3. Why is this project interesting? We took a non-perturbative approach. We solved the problem EXACTLY. This can be useful in understanding processes like fission, fusion, particle emission. The problem is well-formulated but numerically difficult. It is a very general solution of a simple model which can be applied to fields beyond nuclear physics.

4. Energy scales used in this project: Parameters:

5. Example: R 0 Parameters: E =1.1, D =infinity,  =1 Is it “safe” to truncate the model-space to a finite size? It IS “safe” to truncate the model-space to a finite size (if large enough).

6. Growth of Virtual Excitations with n Excitations into the closed channels grow exponentially with “n” (in the vicinity of the wall ). Parameters: E =1.1, D =infinity,  =1

7. The first few R’s and T’s as functions of E A new channel opens at each integral value of E. Away from the thresholds there are bumps. UNEXPECTED → cusps (expected)

8. R 0 and T 0 for different r ’s The wiggles start to smooth out with growing r. Limit of a Structure-less Particle. Tunneling is enhanced by the internal structure (at least for certain regions of E ).

9. R 0 and T 0 for different D ’s As D increases there is, naturally, more reflection and less transmission. Approaches the limit of an infinite wall.

10. Immediate Future Plans 1.Explore resonances that occur away from the channel-thresholds. 2.Study the phase-shifts and time-delays associated with these processes. 3.Now that a mathematical layout of the method is handy, we would like to extend this to a problem which is more general and more realistic.